The Committee Function: An Influence Equation

In legislative systems a bill is commonly considered and reported by an appropriate committee before it is considered on the floor of the house. Since motions on the floor frequently relate to such bills, it is often apposite to refer to a motion's relevant committee. This article presents a mathematical model of the relationship between the relevant committee's divisions on the floor and a motion's probability of passing. Let x be the proportion of the relevant committee voting yea on the floor, z be the proportion of the relevant committee voting nay on the floor, and y be the proportion of the relevant committee neither voting yea nor voting nay on the floor, then a motion's probability of passing is (x2 + y2)/(x2 + y2 + z2). The fit between theory and observation is quite good: six hundred eleven roll calls from the 90th and 91st Congresses have been analyzed; 0.628 of the motions actually passed; and 0.613 of the motions were expected to pass.